PREPRINT: Proving the Derivative of sin(x) Using the Pythagorean Theorem and the Unit Circle

Abstract

The oft-given proof for the derivative of sin(x) is difficult for students to understand, as it relies on the limit of sin(x)/x. Here, a proof of the derivative of the derivative of sin(x) is given which uses only the Pythagorean theorem, the unit circle, the definition of sine and cosine, the definition of the radian measure of an angle, the distance formula, and the power rule for derivatives.

(deposited 2020-11-15)